The formal classification means participants in the fighting between government forces and pro-Russian separatists in the east could eventually be prosecuted for war crimes in international courts.
"Fighting in eastern Ukraine continues to take its toll on civilians, and we urge all sides to comply with international humanitarian law, otherwise known as the law of armed conflict," ICRC director of operations Dominik Stillhart said in a statement.
"These rules and principles apply to all parties to the non-international armed conflict in Ukraine, and impose restrictions on the means and methods of warfare that they may use," he added.
The Swiss-based humanitarian body is the watchdog for the Geneva Conventions, the rules governing conduct in conflict.
The Red Cross uses the term "non-international armed conflict" for civil war.
It underlined that international law obliges warring sides to respect and protect the civilian population and those not — or no longer — participating in hostilities, including the wounded and those detained, who must be treated with dignity.
Stillhart was due in Ukraine on Wednesday for talks on the conflict and to discuss the ongoing repatriation of the bodies of those who died in downing of Malaysia Airlines flight MH17.
The Red Cross underlined that the laws of war require "all possible measures" to be taken to search for the bodies of the dead, prevent the theft of their personal effects and hand them over to relatives for burial.
"The ICRC is prepared to facilitate the movements and activities of the specialists until their work is complete and the remains of all victims have been recovered and identified," Stillhart said.
Pro-Russian rebels have been widely blamed for downing the plane over eastern Ukraine on July 17th, in a tragedy that claimed 298 lives.
They have also been criticised for their handling of the crash site and the victims remains.
The ICRC said that in the wake of the disaster it had contacted both sides to offer its services to help deal with the bodies.
It said it had already stated its views to both sides in the conflict.
This was its first public statement on the issue, however.